Research Project Supported by NASA Ames: NAG2-1238

Starting Date: November 1998.

NASA Ames Point of Contact: Dr. Timothy Barth

Scalable Numerical Algorithms on Non-Heterogeneous Computing Environment with Dynamic Routing and Load Balancing

PI: Tony F. Chan

Other personel: Petr Vanek, Justin Wan.

Research Goal Summary: We propose to investigate scalable numerical algorithms, primarily multigrid and domain decomposition algorithms, for elliptic and hyperbolic PDE discretizations on non-heterogeneous computing environments. Particular attention and consideration will be given to the design and implementation of scalable algorithms in the presence of dynamic adaptive routing and load balancing. When feasible, prototype algorithms will be benchmarked and evaluated on parallel computing systems at NASA Ames utilizing Code IC and IN developed dynamic routing and load balancing software.

Recent Reports:

(00-10) Tony F Chan and Petr Vanek , Detection of strong coupling in algebraic multigrid solvers , UCLA Math Dept CAM Report 00-10, March 2000. Invited paper at the European Multigrid Conference, Gent, Belgium, September 27-30, 1999.

(99-30) Tony F. Chan and W. L. Wan , Robust Multigrid Methods for Nonsmooth coefficient Elliptic Linear Systems , UCLA Math Dept CAM Report 99-30, Sept. 1999. To appear in J. Comp. Appl. Math. Special Issue "State of the Art of Numerical Analysis", 2000.

(99-29) Petr Vanek, Marian Brezina and Jan Mandel , Convergence of Algebraic Multigrid Based on Smoothed Aggregation , UCLA Math Dept CAM Report 99-29, Sept. 1999.

(99-28) Petr Vanek, Marian Brezina, and Radek Tezaur , Two-Grid Method for Linear Elasticity on Unstructed Meshes , UCLA Math Dept CAM Report 99-28, Sept. 1999.

(99-10) Petr Vanek, Ales Janka and Herve Guillard, Convergence of Algebraic Multigrid Based on Smoothed Aggregation II: Extension to a Petrov-Galerkin Method, UCLA Math Dept CAM Report 99-10, March 1999.

(99-9) Tony F. Chan and Petr Vanek, Multilevel algebraic Elliptic Solvers. UCLA Math Dept CAM Report 99-9, February 1999. Invited paper, in Proc. of High Performance Computing and Networking 1999, Amsterdam, April 1999, Lecture Notes in Comp. Sci. 1593, Springer, pp. 1001-1014.

(98-52) T. Chan, S. Go and J. Zou , Multilevel Spectral Partioning of Unstructured Grids , UCLA Math Dept CAM Report 98-52, December 1998. To appear in Proc. of 11th Int'l Conference on Domain Decomposition Methods, Greenwich, UK, July 1998.

(98-6) W.L. Wan, Tony F. Chan and Barry Smith, An Energy-Minimizing Interpolation for Robust Multigrid Methods, UCLA Math Dept CAM Report 98-6, February 1998. To appear in SIAM J. Sci. Comp. Invited paper presented at 10th Anniversary GAMM Workshop on Multigrid Methods, Oct 1998, Bonn.